Reduced navier stokes in mathematica help please

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reduced navier stokes in mathematica urgent help please

ok I am modelling airflow in the upper airway for application i obstructive sleep apnoea, but I have hit a brick wall with mathematica. I have a system of 3 differential equations with boundary conditions, and I need to solve to find 3 unknown functions numerically so that they may be plotted in various graphs.

The equations are as follows:

D[a[x]*u[x], x] == 0,
u[x] u'[x] == -p'[x],
p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]).

with boundary conditions:

u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1.

so initially I tried to use NDSolve like so..

NDSolve[{D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], 
  p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]), u[0] == 0.1, 
  a[0] == 1, a[10] == 1, p[10] == 1}, {a}, {x, 0, 10}]

but mathematica does this:

Power::infy: "Infinite expression 1/0.^(3/2) encountered. "
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>
General::stop: Further output of Infinity::indet will be suppressed during this calculation. >>
NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.`. >>

which is super annoying, any pointers as to where I'm going wrong would be great. I'm not even sure if I should be using NDSolve so let me know what you think.
thanks in advance
a.

 

[NateD]

You can try using the NDSolveValue function instead. This function should help to avoid the Power::infy error. You can also use the Method option to specify the numerical method you want to use: sol = NDSolveValue[{D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]), u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1}, {a}, {x, 0, 10}, Method -> "ExplicitRungeKutta"];You can then plot the solution with:Plot[sol[x], {x, 0, 10}]